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Many folks, myself included, also believe it's a good idea to have a separate registrar and a separate web host. For the reason that you gave -- and many others, such as one or the other going belly-up, etc., etc.
That said, there seem to be fewer and fewer hosting companies that don't also offer domain registry services -- but that doesn't mean you can't keep them separate.
Said differently, I use a registrar that also offers hosting plans.
I have dedicated hosting with a different company. Their primary business and expertise is web hosting, and they offer domain registration as a convenience to those that may want it.
The two companies shall never meet (unless they merge, then I will change one of them ;-)
For suggestions on selecting a web host, here's one